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Question

A photography book has 60 two sided pages of pictures, each of which is 1/28 inch thick, where each two sided page is preceded by a protective 1/90 inch thick piece of paper, and each side of the book is bound by a 1/6 inch cover. What is the total thickness of the book?

Answer 1

COVERS:  2 x 1/6 = 1/3

 

PAGES:

 

1/28 + 1/90 = (90 + 28)/(90*28) = 118/2520

 

There are 60 of them, so

 

60*118/2520 = 7080/2520 = 708/252  = 354/126 = 177/63 = 59/21

 

You can also use Euclid's Method to reduce it.

708 divided by 252 = 2 remainder 204

252 divided by 204 = 1 remainder 48

204 divided by 48 = 4 remainder 12

48 divided by 12 = 4 remainder 0

 

gcf(708,252) = 12

708/252 divided by 12/12 = 59/21

Note that above we divided by 2, then 2, then 3, or 12.

 

FInally 59/21 + 1/3 = 59/21 + 7/21 = 66/21 = 22/7

 

Interestingly enough, 22/7 = 3.142857142857142857 = 3.142857

which is the fraction that most closely represent pi

 

 

Answer 2

60 pages at (1/28) inch each = 60/28 = 15/7 = 2 1/7 inches

60 protectors at (1/90) inch each = 60/90 = 2/3 inches

2 covers at (1/6) inch each = 2/6 = 1/3 inch

 

Add: 

2 1/7 + 2/3 + 1/3 = 2 1/7 + 1 = 3 1/7 inches thick